Temperature dependence of jump electrical conductivity of semiconductor pyropolymers

Polymer Science U.S.S.R. Vol. 23, 1~o. 10, pp. 2390-2396, 1 9 8 1 Printed in Poland

0032-3950/81[102590-07507.50/0 © 1982 Pergamon Press Ltd.

TEMPERATURE DEPENDENCE OF JUMP ELECTRICAL CONDUCTIVITY OF SEMICONDUCTOR PYROPOLYMERS* 1~. A. MAGRUPOV and U. ABDURAKttMA_~OV Lenin State University, Tashkent (Received 5 .May 1980)

It is shown that the temperature dependence of tim electrical conductivity of semiconductor pyropolymers over a wide te~rtperature range obeys the Mort law. Semiconductors based on pyropolyraers ~nay he modelled by a random net of Miller and Abrahams resistances. Here the donor analogue is provided by the regions of p<)lyeonjugation and the dielectric layers are the analogues of the resistance of the transition of the charge carriers between these regions. THE temperature dependence of the electrical conductivity of semiconductor pyropolymers has been investigated in a number of studies [1-7]. However, the nature of such a dependence is still not clear. This work considers the phenomenon of transfer of charge carriers in semiconductor pyropolymers as exemplified by PAN semiconductors within the framework of the theory of the electronic states of disordered systems [8, 9]. I t is known [8] t h a t the temperature dependence of jump conductivity in the regime of constant activation energy has the form a=~3 ex-p ( - - k ~ )

(1)

From this expression the activation energy ea corresponding to the given temperature is determined by the derivative d (In a)/d(kT) -1. Taking this into account from the Mott law

+]

+

where T o and ao are the parameters of the specifically used model it follows t h a t ~3 monotoaically falls with fall in the temperature proportionately to T ÷ and is expressed by the relation e~= - i~ - £m+hrO+ 0 ~-£ ,

where k is the Boltzmann constant. * Vysokomol. soyed. A23: No. 10, 2199-2203, 1981. 2390

(3)

Electrical conductivity of semiconductor pyropolymers

2391

For To and a0 Mott [10] proposed use of the expressions (4)

T ° = kg (/u)aa

'

2

'

(5)

where a is the radius of the localized states close to the Fermi level; g(/~) is the density of the states at the Fermi level; e is the electron charge; v is the phonon frequency; 40 is a constant of the order of unity and fl= 21.2± 1-2 is a coefficient found from the flow theory [9]. The present work seeks to elucidate the legitimacy of the formulae (1-5) for describing the temperature dependence of the parameters of the electrical conductivity of amorphous semiconductor pyropolymers based on PAN. A P A N film 1 0 - 2 0 / l m t h i c k w a s o b t a i n e d f r o m s o l u t i o n . T h e a n d t h e m e t h o d o f its t h e r m a l t r e a t r a e n t a r e d e s c r i b e d in [11]. T h e p a r a ~ a g n e t i e e e n t r e s N w a s d e t e r m i n e d b y the E S R m e t h o d . T h e v o l u m e t r i c s h a r e Vz o f t h e regions o f p o l y c o n j u g a t i o n is d e s c r i b e d i n a~lcasurements were m a d e i n v a c u o ( ~ 1 × 10 -~ torr).

initial characteristics n u m b e r (spin/era 8) o f d e t e r m i n a t i o n of t h e r e f e r e n c e [12]. All t h e

As Fig. la shows, the temperature dependence of the electrical conductivity in the interval 100-450°K in the coordinates log a-(l/T) ÷ well fits a straight line and hence is described by the Mort law (2). The joint solution of equations (4) and (5) using the data in Fig. la, as m a y be seen from Table 1, gives implausible values both for a and 9(~). Similar results were obtained in the case of polyaeene copolymers of the quinone-radical type [13]. Therefore to determine g(p) as the magnitude a we used half the mean linear dimension S/2 between the regions of semiconjugation. In this case the ~:alues g~u) determined from formula (4) are quite probable while for the relation (5) we obtain results improbable from the physical standpoint (Table 1). Consequently, equation (5) is inapplicable to polymer semiconductors. From Fig. la it will be seen that the temperature dependence of conductivity in narrow temperature regions in the coordinates log a-1/T fits a straight line. The values of % determined from the function log a-liT corresponding to these narrow temperature intervals monotonically fall with fall in temperature (Table 2) and are expressed by the relation (3). To understand the nature of the temperature dependence of the electrical conductivity of semiconductor pyropolymers it is necessary to study their structure. They m a y now be considered as heterogeneous systems consisting of electrically well conducting regions of polyconjugation with dielectric layers between them [1, 2, 5, 7, 14]. Concrete models of such systems which may be used to describe the PAN samples thermolysed at different temperatures arc proposed in reference [14]. The volumetric share of the regions of polyoonjugation is

TABLE

400 500 600

T°

1. D E P E N D E N C E

I- 8 X lO g 6- 7 X lO s l. 13 X 108

To, K

I

0.09

5. 9 x lO 1~ 3 . 5 X 10 ~

6. l x 1014

eV_,.m_ a

1 × 10 -z2 l X 10 ~1 1.7 X ]O-SO 5.7 X 105~ 7 - 1 X 1 0 -~7 4 " 8 X 1 0 4 .

a, m

4.7 2.4 1.3

S12, x X 10 -1° m

OF THERMAL

1 . 3 X lO,a 2. 8 X 1025 6 . 5 X lO is

(4)

]

3"8X 10 ~a

1" 6 X 10 ~4 102a

8"2×

n, m -3

2"4 × 1 0 ' 4" 5 X 10 7 5"7X 104

•V - L s e e - *

TREATIkiENT O F T H E S A M P L E

2.2 X lOSe 4.1 X 10 ' s 2 . 6 X 10 a9

(5)

g(~), d e t e r m i n e d from equation

]2o O N T H E T E M P E R A T U R E

g(/~),

To, O'o,a, g(~), ,¢w/2,• A N D

~ - X . ro.-x

O F 3:Kw. P A R A M E T E I % S

0

2393

Electrical conductivity of semiconductor pyropolymers

fixed by the technology of obtaining pyropolymers and gradually increases with the temperature of thermal treatment of the sample. In the initial stage of formation of the semiconductor properties, the regions of polyconjugation are isolated from each other but with rise in temperature of thermal treatment clusters of them gradually form [15], the individual clusters forming a single spin-system. The distances between the regions of polyconjugation and their clusters must have a set of values since their formation in pyropolymers during pyrolysis of the starting polymer is of a random character. Such inhomogeneous systems may apparently be modelled by a net of random Miller and Abrahams resistances [8, 9]. TABLE 2. DEPENDEI~CE OF THE ACTIVATION E N E R G Y

(gtexp FROM (I) A_~D escape (3) OF P A ~

SE:MICONDUCTOI~SOBTAINED AT 400, 500 AND 600°C ON 'I~HETEMPEI~ATU]gEOF :M_EAS~EM~:NT AT*

I 83¢Xp, eV

gSC&lC~

eV

AT*

P A N 400 112-124 148-162 178-194 210-232 238-280 298--431

O"165 O"190 0, 223 0,257 0,282 0, 364

e3ex p ~

8scale,

eV

eV

P A N 500 0.159 0.191 0"219 0-249 0-28 0.361

105-113 133-147 174--190 230-264 307-425

O. 120 O. 140 O- 170 0.215 0,280

AT* i g~exp~ eV

I gSCalc~ oV

P A N 600 0.114 0.137 0,167 0.210 0.282

102-108 116-126 135-151 168-188 202-232 270-374

0" 072 0, 083 0, 093 0,11 0" 125 (~176

0-077 0, 082 0,093 0, 109 0-127 0,171

* ~T is the temperature interval in which the mean value ofes was determined.

Here, the donor analogue is provided by the regions of polyconjugation and the dielectric layers are the analogue ~)fthe resistances of the transition of the current carriers between these regions. At low temperatures the main contribution to conductivity is made by the resistances with low values of sa. With rise in temperature the resistances with relatively large values of 88 also begin to make a contribution. It is known that the expression for electrical conductivity has the form a=en~

(6)

,

where n and/~ are the concentrations and mobility of the charge carriers, respectively. In the case of semiconductor pyropolymers by n must be understood the mean number of regions of polyconjugation and their clusters within which the barriers for the charge carriers are practically transparent. Therefore n , ~ N . The electrical conductivity, in the main, is determined by the jumps of the charge carriers between the regions of polyconjugation and their clusters. In such semiconductors increase in conductivity with temperature is chiefly related to rise in ~ [2, 5, 6]. Consequently, for the temperature dependence of/~ one may write '

To ÷

,,,

2394

M.A. MAoRm'ov and U. A.~vv~.zxmezNov

From expressions (2), (O) and (7) we have

where P0 is a constant not depending on the temperature of measurement. The values n determined by the technique in reference [15] and/J0 as a function of the temperature of thermal treatment are presented in Table 1. Knowing P0 from equation (7) it is possible to determine the value of mobility of the charge carriers corresponding to the given temperature. As Fig. lb shows with rise in the temperature of thermal treatment/~ rises. 3 [

7 ]

I

11 103,t~K-t

O.2q

I 1t7

I

O'3OT'I,hK 1"#

150 ~

I

C

~-2

1

j

E

,i o=

~17

-/#

50-

2

2

3 I

0.2.5

0~I T'I/~K-~/'J

I

I

L

0.25 061 7--1/,t K-I/~

Fzo. 1. Temperature dependence of electrical conductivity (a), m o b i l i t y of charge carriers (b) and the mean length of j u m p of charge carriers (c) of P A N semicondnctors obtained a t t h e t e m p e r a t u r e of t h e r m a l t r e a t m e n t 400 (1, 1'), 500 (2, 2'), and 600 (3, 3') °C. Curves 1 - 3 and 1"-3" are given in the coordinates log a ~ T -÷ and log cr~T -t, respectively.

Thus, it may be concluded that semiconductor pyropelymers are strongly inhomogeneous systems the conductivity of which over a wide temperature range is that with a variable length of jump. The temperature dependence of the mean length of the jump F is described by the expression [9] r = 2.'73 a As Fig. lc shows, with rise in temperature of thermal treatment of the sample the mean length of the jump decreases. Comparison of the data in Fig. lb and Table 2 shows that to a high value of activation energy corresponds a high vahm of mobility. There is no doubt that the interpretation of the temperature dependence of electrical conductivity developed in this work also holds for all semiconductor pyropolymers. To illustrate this we treated the data in references [4, 5] within the framework of the Mort law (2). As Figs. 2 and 3 show, the curves of the temperature dependence of the electrical conductivity in the coordinates log a - l i T transform into straight lines in the coordinates log ~-(1]T) ~.

2395

Electric~I conductivity of semiconductor pyropolymers

In conclusion it should be noted t h a t this paper has been concerned with a model in which the density of the localized states does not depend on energy. In such a model the region of applicability of the Mott law (2) is limited neither 5 i

;

9 ;03/TrK -t I

I

-2 0.2

O.q T ' t ~ g - ~

7

%

-

1

-IO -50

loo W~T,K -~

F,o. 2

2 I

0.24

0.28

7"'1/~K-t/~

Fzo. 3

Fzo. 2. Temperature dependence of electrical conductivity of P A N semiconductors obtained at the t e m p e r a t u r e of t h e r m a l t r e a t m e n t 800 (1) and 850 (2) °C. 1, 2 - - D a t a of reference [4] in the coordinates log a ~ T - Z ; 1", 2 ' - - s a m e d a t a in t h e coordinates log a ~ T -÷. Fro. 3. Temperature dependence of electrical conductivity of radiation-theITaally modified P E sample with t e m p e r a t u r e of t h e r m a l t r e a t m e n t 445°C iodized at 240°C. 1 - - C u r v e o f Fig. 82 from monograph [5] in the coordinates log a ~ T - l ; 2 - - s a m e data. in the coordinates log a ~ T -÷.

at high nor low temperatures [9]. Since we noted observance of the Mort law over a wide temperature range (10-450°K) it m a y be concluded that in semiconductor pyropolymers a situation is realized in which the density of states over a large temperature region m a y be considered constant. REFERENCES 1. B. E. DAVYDOV, Organicheskiye poluprovodniki (Organic Semiconductors). p. 441, Nauka, Moscow, 1968 2. L. L BOGUSLAVSKII and A. V. VANNIKOV, Organicheskiye poluprovodniki i biopolim e r y (Organic Semiconductors and Biopolymers) l~auka, Moscow, 1968 3. T. H I R A I a n d O. NAKADA, J a p . J. Appl. Phys. 7: 112, 1968 4. H. W. HELRERG and H. WARTENBERG, Phys. Status Solidi AS: 401, 1970 5. N.A. BA]KH, A. V. VANNIKOV and A. D. GRISH]NA, Elektroprovodnost' i paramagnetizm polimernykh poluprovodnikov (Electrical Conductivity and Paramagnotism o f P o l y m e r Semiconductors) Nauka, Moscow, 1971 6. M. SUZUKI, K. T A K A H A S H I and S. MITANI, J a p a n J. Appl. Phys. 14: 741, 1975

2396

V. N. PAVLYUCHENKO et al.

7, J.L. JACQUEMIN, A. ARDALAN and G. BORDURE, J. l~on-Crystal. Solids 28: 249, 1978 8. B. I. SI~KLOVSKII and A. L. EFROS, Uspekh. fiz. n a u k 117: 401, 1975 9. B. I. SHKLOVSKH and E. L. EFROS, Elektronnye svoistva legirovannykh poluprovodnikov (Electronic Properties of Alloyed Semiconductors). l~auka, Moscow, 1979 10. N. F. MOTT, Phil. Mag. 19: 835, 1969 l l . M . A. MAGRUPOV and U. ABDURAKHMANOV, Vysokomol. soyed. B21: 731, 1979 (Not translated in Polymer Sei. U.S.S.R.) ] 2. U. ABDURAKHMANOV and M. A. MAGURPOV, Dokl. Akad. Nauk UzSSR, No. 3, 45, 1980 13. K. SAHA, S. C. ABBI and H. A. POHL, J. Non-Crystal Solids 21: 117, 1976 14. M. A. MAGPUROV and U. ABDURAKHMA_NOV, Vysokomol. soyed. A22: 2279, 1980 (Translated in Polymer Sci. U.S.S.R. 22: 10, 2499, 1980) 15. M. A, MAGPUROV and U. ABDURAKHMANOV, Vysokomol. soyed. B23: 527, 1981 (Not translated in Polymer Sci. U.S.S.R.)

PolymerScienceU.S.S.R. Vol.23, No. 10, pp. 2396-2403, 1981 Printed in Poland

0032-3950/81/102396-08507.50/0 © 1982 PergamonPress Ltd.

STUDY OF THE KINETIC ASPECTS OF EMULSION COPOLYMERIZATION OF BUTYL ACRYLATE WITH THE METHACRYLIC ESTER OF ~-HYDROXYETHYL-TERT-BUTYL PEROXIDE* V. N . PAVIJYUCHENKO,

Z. ~ .

AI, EKSEYEVA a n d S. S. IVANCHEV

OkhtiImk "Plastpolimer" Research Assoeiati()n

(Received 12 May 1980) The authors have studied the emulsion copolymerization of b u t y l acrylate with the methacrylic ester of a-hydroxyethyl-tert-butyl peroxide under the influence of the potassiura pcrsulphate--sodium metabisulphite initiating system in presence of the emulsion stabilizer--Volgonate. I t was established that the rate of copolymerization in the region of low concentrations of the emulsifier does not depend on its concentration; at high concentrations the order of the reaction o11 emulsifier is (~4. rl]he reaction orders for potassiu~rt persulphate and sodium metabisulphite are respectively 1 and 3"6. I t is shown t h a t the reaction rate dependence on the ratio of tile eomonomers passes through a maxixaum, and is explained by the predominance of the processes of flocculation of the particles over the processes of their generation at raised concentrations of the peroxide, which leads to fall in the total rate of eopolymerization. A special feature of copolyraerization of these ~aonomers is the participation of the ~-oxyethyl-tert-butyl peroxide in the reaction of initiation as a component of the initiating system. * V'ysokomol. soyed. A23: No. 10, 2204---2210. 1981.